Hi! Amazing tool - In theory, could it be used for Game Boy development, too?

Thanks! 

In theory, yes. The NES and GB(C) are very similar systems, graphics wise. 
But there are currently several caveats and user requirements. 

You can replace the 'system palette' with a file that represent the 4 gameboy colours. There is no premade solution, but it's fairly simple to make.
NEXXT can also convert NES-format tile characters (.chr) to GB format. 
Other than that, you need to write a bit of scripting to convert other sources.
You also have a limit of 256 tiles per scene, whereas the gameboy has an extra set of tiles shared between background and sprites; so you're currently a bit limited in that sense. Thankfully, level design rarely requires more than that, especially considering the GB:s lower screen resolution.

For Gameboy color, it gets more complicated to try to make it work. NEXXT runs on the assumption of 16x16 pixel-sized attribute cells (the area which a single subpalette must cover), whereas the GBC runs on finer 8x8 (tile-sized) attributes cells. Besides conversion, this makes for coarser colour layouts. 
There's also no support for the full RGB palette, you'd need to pick out an identity of 64 colours externally, import that, and turn off 2 NES-specific emulation rules found in the menu. 

Lastly, you might be interested to know that i'm working on a kickstarter for the the development of NEXXT 4.0, and that one of its first 'stretch goals' is going to be proper gameboy / gbc support, complete with specialized features & a 'gameboy personality' to the GUI. That will remove all the althoughs and buts.

I don't know when that'll launch, but hopefully this autumn.

Many thanks for the detailed reply - what you said echoes my experience, it's *so close* to being what I need but would require a few changes/conversions. Please keep me posted on the Kickstarter, I run Thalamus Digital so I can definitely amplify your campaign on our socials. :)